Quantum lattice gas. Method of density matrix

Abstract

A new thermodynamic method is proposed to study equilibrium states of a quantum many-particle system which is statistically described by virtue of a density matrix. The method is based on the principle of minimum free energy of the equilibrium system. The new feature of the method is that free energy is considered as a functional depending not only on the state distribution function of particles but also on the parameters of the unitary transformation that diagonalize the density matrix. Using this method different models of a lattice gas were studied, which allowed us to give a simple explanation of such cooperative phenomena as condensation (spinodal decomposition), superfluidity, metal-insulator transition, superconductivity, etc. Density matrices describing those phenomena were obtained.